Abstract

We discuss the problem of recognizing permuted Van der Veen (VdV) matrices. It is well known that the TSP with a VdV matrix as distance matrix is pyramidally solvable. In this note we solve the problem of recognizing permuted strong VdV matrices. This yields an O(n(4)) time algorithm for the TSP with a permuted Euclidean VdV matrix. The problem, however, of recognizing permuted VdV matrices in general remains open. (C) 2004 Elsevier B.V. All rights reserved.